The problem of non-Gaussian noise/outliers has been intrinsic in modern Simultaneous Localization and Mapping (SLAM) applications. Despite numerous algorithms in SLAM, it has become crucial to address this problem in the realm of modern robotics applications. This work focuses on addressing the above-mentioned problem by incorporating the usage of correntropy in SLAM. Before correntropy, multiple attempts of dealing with non-Gaussian noise have been proposed with significant progress over time but the underlying assumption of Gaussianity might not be enough in real-life applications in robotics.Most of the modern SLAM algorithms propose the `best' estimates given a set of sensor measurements. Apart from addressing the non-Gaussian problems in a SLAM system, our work attempts to address the more complex part concerning SLAM: (a) If one of the sensors gives faulty measurements over time (`Faulty' measurements can be non-Gaussian in nature), how should a SLAM framework adapt to such scenarios? (b) In situations where there is a manual intervention or a 3rd party attacker tries to change the measurements and affect the overall estimate of the SLAM system, how can a SLAM system handle such situations?(addressing the Self Security aspect of SLAM). Given these serious situations how should a modern SLAM system handle the issue of the previously mentioned problems in (a) and (b)? We explore the idea of correntropy in addressing the above-mentioned problems in popular filtering-based approaches like Kalman Filters(KF) and Extended Kalman Filters(EKF), which highlights the `Localization' part in SLAM. Later on, we propose a framework of fusing the odometeries computed individually from a stereo sensor and Lidar sensor (Iterative Closest point Algorithm (ICP) based odometry). We describe the effectiveness of using correntropy in this framework, especially in situations where a 3rd party attacker attempts to corrupt the Lidar computed odometry. We extend the usage of correntropy in the `Mapping' part of the SLAM (Registration), which is the highlight of our work. Although registration is a well-established problem, earlier approaches to registration are very inefficient with large rotations and translation. In addition, when the 3D datasets used for alignment are corrupted with non-Gaussian noise (shot/impulse noise), prior state-of-the-art approaches fail. Our work has given birth to another variant of ICP, which we name as Correntropy Similarity Matrix ICP (CoSM-ICP), which is robust to large translation and rotations as well as to shot/impulse noise. We verify through results how well our variant of ICP outperforms the other variants under large rotations and translations as well as under large outliers/non-Gaussian noise. In addition, we deploy our CoSM algorithm in applications where we compute the extrinsic calibration of the Lidar-Stereo sensor as well as Lidar-Camera calibration using a planar checkerboard in a single frame. In general, through results, we verify how efficiently our approach of using correntropy can be used in tackling non-Gaussian noise/shot noise/impulse noise in robotics applications
